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SMO 2018 Senior Round 1 Question 1

SMO · SMO 2018 Senior Round 1

Question 1

The roots of the quadratic equation $x^2-3 x+1=0$ are $\alpha$ and $\beta$. Find a quadratic equation whose roots are $\alpha^2+\alpha$ and $\beta^2+\beta$.
  1. $x^2+10 x-5=0$
  2. $x^2-10 x+5=0$
  3. $x^2-5 x-10=0$
  4. $x^2+5 x-10=0$
  5. $x^2-5 x-5=0$